Mon. Not. R. Astron. Soc. 000, 1–20 (2009)
Printed 19 November 2009
(MN LATEX style file v2.2)
arXiv:0909.4307v2 [astro-ph.SR] 19 Nov 2009
Precise mass and radius values for the white dwarf and low mass M dwarf in the pre-cataclysmic binary NN Serpentis S. G. Parsons1⋆ , T. R. Marsh1, C. M. Copperwheat1, V. S. Dhillon2, S. P. Littlefair2, B. T. G¨ansicke1 and R. Hickman1 1 Department of Physics, University of Warwick, Coventry, CV4 7AL of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH
2 Department
Accepted 2009 November 18. Received 2009 November 17; in original form 2009 September 22
ABSTRACT
Using the high resolution Ultraviolet and Visual Echelle Spectrograph (UVES) mounted on the Very Large Telescope (VLT) in combination with photometry from the high-speed CCD camera ULTRACAM, we derive precise system parameters for the pre-cataclysmic binary, NN Ser. A model fit to the ULTRACAM light curves gives the orbital inclination as i= 89.6◦ ± 0.2◦ and the scaled radii, RWD /a and Rsec /a. Analysis of the HeII 4686˚ A absorption line gives a radial velocity amplitude for the white dwarf of KWD = 62.3 ± 1.9 km s−1 . We find that the irradiation-induced emission lines from the surface of the secondary star give a range of observed radial velocity amplitudes due to differences in optical depths in the lines. We correct these values to the centre of mass of the secondary star by computing line profiles from the irradiated face of the secondary star. We determine a radial velocity of Ksec = 301 ± 3 km s−1 , with an error dominated by the systematic effects of the model. This leads to a binary separation of a = 0.934±0.009 R⊙ , radii of RWD = 0.0211±0.0002 R⊙ and Rsec = 0.149±0.002 R⊙ and masses of MWD = 0.535 ± 0.012 M⊙ and Msec = 0.111 ± 0.004 M⊙ . The masses and radii of both components of NN Ser were measured independently of any massradius relation. For the white dwarf, the measured mass, radius and temperature show excellent agreement with a ‘thick’ hydrogen layer of fractional mass MH /MWD = 10−4 . The measured radius of the secondary star is 10% larger than predicted by models, however, correcting for irradiation accounts for most of this inconsistency, hence the secondary star in NN Ser is one of the first precisely measured very low mass objects (M . 0.3 M⊙ ) to show good agreement with models. ULTRACAM r’, i’ and z’ photometry taken during the primary eclipse determines the colours of the secondary star as (r’-i’ )sec = 1.4 ± 0.1 and (i’-z’ )sec = 0.8 ± 0.1 which corresponds to a spectral type of M4 ± 0.5. This is consistent with the derived mass, demonstrating that there is no detectable heating of the unirradiated face, despite intercepting radiative energy from the white dwarf which exceeds its own luminosity by over a factor of 20. Key words: binaries: eclipsing – stars: fundamental parameters – stars: late-type – white dwarfs – stars: individual: NN Ser
1
INTRODUCTION
Precise measurements of masses and radii are of fundamental importance to the theory of stellar structure and evolution. Mass-radius relations are routinely used to estimate the masses and radii of stars and stellar remnants, such as white dwarfs. Additionally, the mass-radius relation for white dwarfs has played an important role in estimating the distance to globular clusters (Renzini et al. 1996) and the
⋆
[email protected]
determination of the age of the galactic disk (Wood 1992). However, the empirical basis for this relation is uncertain (Schmidt 1996) as there are very few circumstances where both the mass and radius of a white dwarf can be measured independently and with precision. Provencal et al. (1998) used Hipparcos parallaxes to determine the radii for 10 white dwarfs in visual binaries or common proper-motion (CPM) systems and 11 field white dwarfs. They were able to improve the radii measurements for the white dwarfs in visual binaries and CPM systems. However, they remarked that mass determinations for field
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white dwarfs are indirect, relying on complex model atmosphere predictions. They were able to support the massradius relation on observational grounds more firmly, though they explain that parallax remains a dominant source of uncertainty, particularly for CPM systems. Improvements in our knowledge of the masses and radii of white dwarfs requires additional measurements. One situation where this is possible is in close binary systems. In these cases, masses can be determined from the orbital parameters and radii from light-curve analysis. Of particular usefulness in this regard are eclipsing post-common envelope binaries (PCEBs). The binary nature of these objects helps determine accurate parameters and, since they are detached, they lack the complications associated with interacting systems such as cataclysmic variables. The inclination of eclipsing systems can be constrained much more strongly than for non-eclipsing systems. Furthermore, the distance to the system does not have to be known, removing the uncertainty due to parallax. An additional benefit of studying PCEBs is that under favourable circumstances, not only are the white dwarf’s mass and radius determined independently of any model, so too are the mass and radius of its companion. These are often low mass late-type stars, for which there are few precise mass and radius measurements. There is disagreement between models and observations of low mass stars; the models tend to under predict the radii by as much as 20-30% (L´ opez-Morales 2007). Hence detailed studies of PCEBs can lead to improved statistics for both white dwarfs and low mass stars. Furthermore, models of low mass stars are important for understanding the late evolution of mass transferring binaries such as cataclysmic variables (Littlefair et al. 2008). The PCEB NN Ser (PG 1550+131) is a low mass binary system consisting of a hot white dwarf primary and a cool M dwarf secondary. It was discovered in the Palomar Green Survey (Green et al. 1982) and first studied in detail by Haefner (1989) who presented an optical light curve showing the appearance of a strong heating effect and very deep eclipses (>4.8mag at λ ∼ 6500 ˚ A). Haefner identified the system as a pre-cataclysmic binary with an orbital period of 0.13d. The system parameters were first derived by Wood & Marsh (1991) using low-resolution ultra-violet spectra then refined by Catalan et al. (1994) using higher resolution optical spectroscopy. Haefner et al. (2004) further constrained the system parameters using the FORS instrument at the Very Large Telescope (VLT) in combination with high-speed photometry and phase-resolved spectroscopy. However, they did not detect the secondary eclipse leading them to underestimate the binary inclination and hence overestimate the radius and ultimately the mass of the secondary star. They were also unable to directly measure the radial velocity amplitude of the white dwarf and were forced to rely upon a mass-radius relation for the secondary star. Recently, Brinkworth et al. (2006) performed high time resolution photometry of NN Ser using the highspeed CCD camera ULTRACAM mounted on the William Herschel Telescope (WHT). They detected the secondary eclipse leading to a better constraint on the inclination, and also detected a decrease in the orbital period which they determined was due either to the presence of a third body, or to a genuine angular momentum loss. Since NN Ser belongs to the group of PCEBs which is representative for the
Table 1. Journal of VLT/UVES spectroscopic observations. Date
Start (UT)
End (UT)
No. of spectra
Conditions (Transparency, seeing)
30/04/2004 01/05/2004 17/05/2004 26/05/2004 27/05/2004 10/06/2004 12/06/2004 15/06/2004 27/06/2004
05:15 03:14 03:37 00:52 03:14 02:06 02:39 02:41 03:54
08:30 06:31 06:58 04:14 06:42 05:22 05:54 05:56 05:11
40 40 40 40 40 40 40 40 15
Fair, ∼2.5 arcsec Variable, 1.2-3.1 arcsec Fair, ∼2.1 arcsec Fair, ∼2.2 arcsec Good, ∼1.1 arcsec Good, ∼1.1 arcsec Fair, ∼2.1 arcsec Good, ∼1.8 arcsec Fair, ∼2.2 arcsec
progenitors of the current cataclysmic variable (CV) population (Schreiber & G¨ ansicke 2003), the system parameters are important from both an evolutionary point of view as well as providing independent measurements of the masses and radii of the system components. In this paper we present high resolution VLT/UVES spectra and high time resolution ULTRACAM photometry of NN Ser. We use these to determine the system parameters directly and independently of any mass-radius relations. We compare our results with models of white dwarfs and low mass stars.
2 2.1
OBSERVATIONS AND THEIR REDUCTION Spectroscopy
Spectra were taken in service mode over nine different nights between 2004 April and June using the Ultraviolet and Visual Echelle Spectrograph (UVES) installed at the European Southern Observatory Very Large Telescope (ESO VLT) 8.2m telescope unit on Cerro Paranal in Chile (Dekker et al. 2000). In total 335 spectra were taken in each arm, details of these observations are listed in Table 1. Observation times were chosen to cover a large portion of the orbital cycle and an eclipse was recorded on each night. Taken together the observations cover the whole orbit of NN Ser. Exposure times of 250.0s and 240.0s were used for the blue and red spectra respectively; these were chosen as a compromise between orbital smearing and signal-to-noise ratio (S/N ). The wavelength range covered is 3760–4990˚ A in the blue arm and 6710–8530 and 8670–10400˚ A in the red arm. The reduction of the raw frames was conducted using the most recent release of the UVES Common Pipeline Library (CPL) recipes (version 4.1.0) within ESORex, the ESO Recipe Execution Tool, version 3.6.8. The standard recipes were used to optimally extract each spectrum. A ThAr arc lamp spectrum was used to wavelength calibrate the spectra. Master response curves were used to correct for detector response and initially flux calibrate the spectra since no standard was observed. The spectra have a resolution of R∼80,000 in the blue and R∼110,000 in the red. Orbital smearing limits the maximum resolution; at conjunction lines will move by at most ∼ 37 km s−1 . Since the widths of the lines seen in the spectra are at least ∼ 100 km s−1 , this effect is not large. The S/N becomes progressively worse at longer wavelengths and a large region of the upper red CCD spectra was ignored since there was very little signal. The orbital
Precice mass and radius values for both components of the pre-CV NN Ser
3
where c and O are constants and λn is the central wavelength of order n, gives us the phase. We find values of O = 125 and c = 465700, which are similar for all the spectra. Therefore the phase of the ripple is φ = 125 −
465700 . λ
Since the phase is now known, Equation 1 reduces to a simple linear fit. Figure 1 is a normalised average of all the UVES blue arm spectra with the blaze removed. Since this is only a simple fit some residual pattern does remain after division by the blaze function but overall the effect is greatly reduced.
2.3
Figure 1. Averaged, normalised UVES blue arm spectrum with the blaze removed. IS corresponds to interstellar absorption features. The discontinuity at ∼ 4150˚ A and the emission-like feature A are most likely instrumental features or artifacts of at ∼ 4820˚ the UVES reduction pipeline as they are seen in all 335 spectra.
phase of each spectrum was calculated using the ephemeris of Brinkworth et al. (2006). The spectral features seen are similar to those reported by Catalan et al. (1994) and Haefner et al. (2004): Balmer lines, which appear as either emission or absorption depending upon the phase, HeI and CaII emission lines and HeII 4686˚ A in absorption. The Paschen series is also seen in emission in the far red. In addition, MgII 4481˚ A emission is seen as well as a number of fainter MgII emission lines beyond 7800˚ A . Weak FeI emission lines are seen throughout the spectrum and faint CI emission is seen beyond 8300˚ A (see Table 4 for a full list of identified emission lines). The strength of all the emission lines is phase-dependent, peaking at phase 0.5, when the heated face of the secondary star is in full view, then disappearing around the primary eclipse. Several sharp absorption features are observed not to move over the orbital period, these are interstellar absorption features and include interstellar CaII absorption.
2.2
Blaze Removal
An echelle grating produces a spectrum that drops as one moves away from the blaze peak, this is known as the blaze function. After reduction a residual ripple pattern was visible in the blue spectra corresponding to the blaze function. This was approximately removed by fitting with a sinusoid of the form B(λ)
=
a0 + a1 sin(2πφ) + a2 λ sin(2πφ)
(1)
+ a3 cos(2πφ) + a4 λ cos(2πφ). The phase (φ) was calculated by identifying the central wavelength of each echelle order. The line table produced using the ESORex recipe uves cal wavecal provided this information. Then using the relation λn (O − n) = c,
(2)
Photometry
The data presented here were collected with the high speed CCD camera ULTRACAM (Dhillon et al. 2007), mounted as a visitor instrument on the 4.2m William Herschel Telescope (WHT) and on the VLT in June 2007. A total of ten observations were made in 2002 and 2003, and these data were supplemented with observations made at a rate of ∼ 1 – 2 a year up until 2008. ULTRACAM is a triple beam camera and most of our observations were taken simultaneously through the SDSS u’, g’ and i’ filters. In a number of instances an r’ filter was used in place of i’ ; this was mainly for scheduling reasons. Additionally, a z’ filter was used in place of i’ for one night in 2003. A complete log of the observations is given in Table 2. We windowed the CCD in order to achieve an exposure time of 2 – 3s, which we varied to account for the conditions. The dead time was ∼ 25ms. All of these data were reduced using the ULTRACAM pipeline software. Debiassing, flatfielding and sky background subtraction were performed in the standard way. The source flux was determined with aperture photometry using a variable aperture, whereby the radius of the aperture is scaled according to the FWHM. Variations in observing conditions were accounted for by determining the flux relative to a comparison star in the field of view. There were a number of additional stars in the field which we used to check the stability of our comparison. For the flux calibration we determined atmospheric extinction coefficients in the u’, g’ and r’ bands and subsequently determined the absolute flux of our targets using observations of standard stars (from Smith et al. 2002) taken in twilight. We use this calibration for our determinations of the apparent magnitudes of the two sources, although we present all light curves in flux units determined using the conversion given in Smith et al. (2002). Using our absorption coefficients we extrapolate all fluxes to an airmass of 0. The systematic error introduced by our flux calibration is < 0.1 mag in all bands. For all data we convert the MJD times to the barycentric dynamical timescale, corrected to the solar system barycentre. A number of comparison stars were observed, their locations are shown in Figure 2 and details of these stars are given in Table 3. Where possible we use comparison star C since it is brighter. However, in 2002 only comparison star D was observed and in the 2007 VLT data, comparison stars C and B were saturated in g’ and i’. We therefore use star C for the comparison in the u’ and star A for the g’ and i’. The light curves were corrected for extinction differ-
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Table 2. ULTRACAM observations of NN Ser. The primary eclipse occurs at phase 1, 2 etc. Date
Filters
Telescope
UT start
UT end
Average exp time (s)
Phase range
Conditions (Transparency, seeing)
17/05/2002 18/05/2002 19/05/2002 20/05/2002 19/05/2003 21/05/2003 22/05/2003 24/05/2003 25/05/2003 03/05/2004 04/05/2004 09/03/2006 10/03/2006 09/06/2007 16/06/2007 17/06/2007 07/08/2008
u’g’r’ u’g’r’ u’g’r’ u’g’r’ u’g’z’ u’g’i’ u’g’i’ u’g’i’ u’g’i’ u’g’i’ u’g’i’ u’g’r’ u’g’r’ u’g’i’ u’g’i’ u’g’i’ u’g’r’
WHT WHT WHT WHT WHT WHT WHT WHT WHT WHT WHT WHT WHT VLT VLT VLT WHT
21:54:40 21:21:20 23:58:22 00:58:23 22:25:33 00:29:00 03:24:57 22:58:55 01:29:45 22:13:44 23:18:46 01:02:34 05:01:13 04:59:25 03:57:48 01:50:16 23:41:29
02:07:54 02:13:17 00:50:52 01:57:18 01:02:25 04:27:32 03:50:40 23:33:49 02:15:58 05:43:11 23:56:59 06:46:49 05:50:14 05:46:18 04:54:39 02:38:09 00:22:46
2.4 3.9 2.0 2.3 6.7 1.9 2.0 2.0 2.0 2.5 2.5 2.0 2.0 0.9 2.0 1.0 2.8
0.85–2.13 0.39–1.23 0.93–1.10 0.86–1.14 0.47–1.12 0.32–0.59 0.36–0.08 0.90–0.08 0.39–0.64 0.37–2.27 0.91–0.61 0.91–2.70 0.85–1.11 0.40–0.61 0.86–1.15 0.86–1.11 0.87–1.07
Good, ∼1.2 arcsec Variable, 1.2-2.4 arcsec Fair, ∼2 arcsec Fair, ∼2 arcsec Variable, 1.5-3 arcsec Excellent, ∼1 arcsec Excellent,
